Kentucky was unranked in 15 of the final 16 weeks of last season and lost in the first round of the NIT to Robert Morris.
It is just the third time Kentucky has started the season ranked No. 1 by AP.
The ACC has the most teams in the top 25 with five. They include No. 4 Duke, No. 8 Syracuse, No. 13 North Carolina, No. 21 Notre Dame and No. 24 Virginia. Syracuse and Notre Dame are among the conference's new members following the breakup of the Big East.
The Big Ten includes four ranked teams, and the Big 12, Pac-12 and American Athletic Conference each have three.
More than 130 games kick off the season on Nov. 8. The first tournament is the four-team Champions Classic in Chicago on Nov. 12 and the 16-team NIT Season Tip-Off at Madison Square Garden in New York starts Nov. 18.